The predictive ratio is considered as a measure of spread for the predictive distribution. It is shown that, in the exponential families, ordering according to the predictive ratio is equivalent to ordering according to the posterior covariance matrix of the parameters. This result generalizes an inequality due to Chaloner and Duncan who consider the predictive ratio for a beta-binomial distribution and compare it with a predictive ratio for the binomial distribution with a degenerate prior. The predictive ratio at x1 and x2 is defined to be pg(x1)pg(x2)/[pg()]2 = hg(x1, x2), where pg(x1) = [integral operator] [latin small letter f with hook](x1[short parallel][theta]) g([theta]) d[theta] is the predictive distribution of x1 with respect to the prior g. We prove that hg(x1, x2) >= hg*(x1, x2) for all x1 and x2 if [latin small letter f with hook](x[short parallel][theta]) is in the natural exponential family and Covg[short parallel]x([theta]) >= Covg*[short parallel]x([theta]) in the Löwner sense, for all x on a straight line from x1 to x2. We then restrict the class of prior distributions to the conjugate class and ask whether the posterior covariance inequality obtains if g and g* differ in that the "sample size"

If you experience problems downloading a file, check if you have the
proper application to
view it first. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6WK9-4CRMBSM-NV/2/56cc1d01c9d554223ad4abb48f597acdDownload Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:33:y:1990:i:2:p:275-285. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through
the various RePEc services.